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International Journal of Computer Mathematics Volume 86, 2009 - Issue 9
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Section B

High-accuracy cubic spline alternating group explicit methods for 1D quasi-linear parabolic equationsFootnote†

R. K. Mohanty Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, IndiaCorrespondence[email protected]
&
M. K. Jain Department of Mathematics, Indian Institute of Technology, New Delhi, IndiaView further author information
Pages 1556-1571 | Received 25 Jan 2007, Accepted 08 Jan 2008, Published online: 22 Jul 2009

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Sachin Sharma & Naina Sharma. (2024) A fast computational technique to solve fourth-order parabolic equations: application to good Boussinesq, Euler-Bernoulli and Benjamin-Ono equations. International Journal of Computer Mathematics 101:2, pages 194-216.
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R. K. Mohanty, Kajal Mittal & Deepti Kaur. (2021) A new high accuracy off-step cubic spline approximations on a quasi-variable mesh for the system of nonlinear parabolic equations in one space dimension. International Journal for Computational Methods in Engineering Science and Mechanics 22:2, pages 123-137.
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R. K. Mohanty, Ravindra Kumar & Nikita Setia. (2021) Cubic spline approximation based on half-step discretization for 2D quasilinear elliptic equations. International Journal for Computational Methods in Engineering Science and Mechanics 22:1, pages 45-59.
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Articles from other publishers (20)

R. K. Mohanty & Divya Sharma. (2024) A new 2-level implicit high accuracy compact exponential approximation for the numerical solution of nonlinear fourth order Kuramoto–Sivashinsky and Fisher–Kolmogorov equations. Journal of Mathematical Chemistry 62:5, pages 973-1011.
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Anshima Singh, Sunil Kumar & Jesus Vigo-Aguiar. (2023) A fully discrete scheme based on cubic splines and its analysis for time-fractional reaction–diffusion equations exhibiting weak initial singularity. Journal of Computational and Applied Mathematics 434, pages 115338.
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R. K. Mohanty & Divya Sharma. (2023) A new 2-level compact off-step implicit method in exponential form for the solution of fourth order nonlinear parabolic equations. Journal of Mathematical Chemistry 61:5, pages 1165-1204.
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R. K. Mohanty & Sachin Sharma. (2020) A new high-accuracy method based on off-step cubic polynomial approximations for the solution of coupled Burgers’ equations and Burgers–Huxley equation. Engineering with Computers 37:4, pages 3049-3066.
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Ranjan Kumar Mohanty & Sachin Sharma. (2020) A high-resolution method based on off-step non-polynomial spline approximations for the solution of Burgers-Fisher and coupled nonlinear Burgers’ equations. Engineering Computations 37:8, pages 2785-2818.
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R. K. Mohanty & S. Sharma. (2020) Fourth-Order Numerical Scheme Based on Half-Step Non-Polynomial Spline Approximations for 1D Quasi-Linear Parabolic Equations. Numerical Analysis and Applications 13:1, pages 68-81.
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Ranjan Kumar Mohanty & Gunjan Khurana. (2019) A new high accuracy cubic spline method based on half-step discretization for the system of 1D non-linear wave equations. Engineering Computations 36:3, pages 930-957.
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Nur Aliah Izzati Rosman, Nur Nadiah Abd Hamid, Ahmad Abd. Majid & Ahmad Izani Md. Ismail. B-spline alternating group explicit (BSPAGE) in solving heat equation. B-spline alternating group explicit (BSPAGE) in solving heat equation.
R. K. Mohanty, Sachin Sharma & Swarn Singh. (2018) A New Two-Level Implicit Scheme for the System of 1D Quasi-Linear Parabolic Partial Differential Equations Using Spline in Compression Approximations. Differential Equations and Dynamical Systems 27:1-3, pages 327-356.
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RK Mohanty & Sachin Sharma. (2017) High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations. Advances in Difference Equations 2017:1.
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RK Mohanty & Gunjan Khurana. (2017) A new spline in compression method of order four in space and two in time based on half-step grid points for the solution of the system of 1D quasi-linear hyperbolic partial differential equations. Advances in Difference Equations 2017:1.
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R. K. Mohanty, Weizhong Dai & Don Liu. (2015) Operator compact method of accuracy two in time and four in space for the solution of time dependent Burgers-Huxley equation. Numerical Algorithms 70:3, pages 591-605.
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R.K. Mohanty, Weizhong Dai & Fei Han. (2015) Compact operator method of accuracy two in time and four in space for the numerical solution of coupled viscous Burgers’ equations. Applied Mathematics and Computation 256, pages 381-393.
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Jalil Rashidinia & Ali Barati. (2015) Numerical solutions of one-dimensional non-linear parabolic equations using Sinc collocation method. Ain Shams Engineering Journal 6:1, pages 381-389.
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R.K. Mohanty & Venu Gopal. (2014) High accuracy non-polynomial spline in compression method for one-space dimensional quasi-linear hyperbolic equations with significant first order space derivative term. Applied Mathematics and Computation 238, pages 250-265.
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Jyoti Talwar & R. K. Mohanty. (2014) A new modified group explicit iterative method for the numerical solution of time dependent viscous Burgers' equation. International Journal of Modeling, Simulation, and Scientific Computing 05:02, pages 1350029.
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R. K. Mohanty, M. K. Jain & Suruchi Singh. (2013) A new three-level implicit cubic spline method for the solution of 1D quasi-linear hyperbolic equations. Computational Mathematics and Modeling 24:3, pages 452-470.
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R.K. Mohanty, M.K. Jain & Deepika Dhall. (2013) High accuracy cubic spline approximation for two dimensional quasi-linear elliptic boundary value problems. Applied Mathematical Modelling 37:1-2, pages 155-171.
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R.K. Mohanty & Venu Gopal. (2011) High accuracy cubic spline finite difference approximation for the solution of one-space dimensional non-linear wave equations. Applied Mathematics and Computation 218:8, pages 4234-4244.
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R.K. Mohanty. (2009) A variable mesh C-SPLAGE method of accuracy for 1D nonlinear parabolic equations. Applied Mathematics and Computation 213:1, pages 79-91.
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